{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.gridspec as gridspec\n",
    "from IPython import display\n",
    "plt.rcParams['image.cmap'] = 'gray'\n",
    "plt.rcParams['image.interpolation'] = 'nearest'\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import os\n",
    "import sys\n",
    "import json\n",
    "import time\n",
    "import numpy as np\n",
    "from random import shuffle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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E0Xad6uWG4qi13CWbNL2wY4iSkza0eJ+D58c32lk03tOibLGuAbp9TcstbEHesvVom9SE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\nkLo+rX7e7oh1TBqwAvgkTAghBeEgTAg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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1064df0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# generate a toy 2D regression dataset\n",
    "sz = 100\n",
    "X,Y = np.meshgrid(np.linspace(-1,1,sz),np.linspace(-1,1,sz))\n",
    "mux,muy,sigma=0.3,-0.3,4\n",
    "G1 = np.exp(-((X-mux)**2+(Y-muy)**2)/2.0*sigma**2)\n",
    "mux,muy,sigma=-0.3,0.3,2\n",
    "G2 = np.exp(-((X-mux)**2+(Y-muy)**2)/2.0*sigma**2)\n",
    "mux,muy,sigma=0.6,0.6,2\n",
    "G3 = np.exp(-((X-mux)**2+(Y-muy)**2)/2.0*sigma**2)\n",
    "mux,muy,sigma=-0.4,-0.2,3\n",
    "G4 = np.exp(-((X-mux)**2+(Y-muy)**2)/2.0*sigma**2)\n",
    "G = G1 + G2 - G3 - G4\n",
    "fig,ax = plt.subplots()\n",
    "im = ax.imshow(G, vmin=-1, vmax=1, cmap='jet')\n",
    "#plt.axis('off')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AAAAOmPtv6Zwd/q94ez7G3b6Vyf+d2LD8xu22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\n46zEsH2uGF8X9z0/y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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1081abda0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(3)\n",
    "nn = 4 # number of steps to take (and plot horizontally)\n",
    "alpha = 0.03 # learning rate\n",
    "sigma = 3 # standard deviation of the samples around current parameter vector\n",
    "\n",
    "w = np.array([70.0, 60.0]) # start point\n",
    "plt.figure(figsize=(20,5))\n",
    "\n",
    "prevx, prevy = [], []\n",
    "for q in range(nn):\n",
    "    \n",
    "    # draw the optimization landscape\n",
    "    ax1 = plt.subplot(1,nn,q+1)\n",
    "    plt.imshow(G, vmin=-1, vmax=1, cmap='jet')\n",
    "\n",
    "    # draw a population of samples in black\n",
    "    noise = np.random.randn(200, 2)\n",
    "    wp = np.expand_dims(w, 0) + sigma*noise\n",
    "    x,y = zip(*wp)\n",
    "    plt.scatter(x,y,4,'k', edgecolors='face')\n",
    "\n",
    "    # draw the current parameter vector in white\n",
    "    plt.scatter([w[0]],[w[1]],40,'w', edgecolors='face')\n",
    "\n",
    "    # draw estimated gradient as white arrow\n",
    "    R = np.array([G[int(wi[1]), int(wi[0])] for wi in wp])\n",
    "    R -= R.mean()\n",
    "    R /= R.std() # standardize the rewards to be N(0,1) gaussian\n",
    "    g = np.dot(R, noise)\n",
    "    u = alpha * g\n",
    "    plt.arrow(w[0], w[1], u[0], u[1], head_width=3, head_length=5, fc='w', ec='w')\n",
    "    plt.axis('off')\n",
    "    plt.title('iteration %d, reward %.2f' % (q+1, G[int(w[0]), int(w[1])]))\n",
    "    \n",
    "    # draw the history of optimization as a white line\n",
    "    prevx.append(w[0])\n",
    "    prevy.append(w[1])\n",
    "    if len(prevx) > 0:\n",
    "        plt.plot(prevx, prevy, 'wo-')\n",
    "    \n",
    "    w += u\n",
    "    plt.axis('tight')\n",
    "    \n",
    "#plt.savefig('evo.png',bbox_inches='tight',pad_inches=0,dpi=200)"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [conda env:py35]",
   "language": "python",
   "name": "conda-env-py35-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
